Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long n, i, l, h, m, f;
  scanf("%I64d", &n);
  for (i = 1; i * i <= 2 * n; i++) {
    f = 0;
    l = 1;
    h = n;
    while (l <= h) {
      m = (l + h) / 2;
      if ((i * (i + 1) / 2) + (m * (m + 1) / 2) == n) {
        f = 1;
        break;
      } else if ((i * (i + 1) / 2) + (m * (m + 1) / 2) < n) {
        l = m + 1;
      } else if ((i * (i + 1) / 2) + (m * (m + 1) / 2) > n) {
        h = m - 1;
      }
    }
    if (f) break;
  }
  if (f)
    printf("YES");
  else
    printf("NO");
  return 0;
}